Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic31⋊C5 |
| unambiguous semidirect product | (C32×Dic31)⋊C5 |
| derived, Sylow | C31 ⋊ C32×C4×C5 |
| Hall | C32×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C32×Dic31 ⋊ C5 |
| Hall | C32×C31 ⋊ C4×C5 |
| Hall | ΓL(1,𝔽32) ⋊ C32×C4 |
| Hall | Dic31 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D31⋊C5 |
| commutator, hypocenter | C31 | C32×C4×C5 |
| Frattini | C2 | C32×D31⋊C5 |
| Fitting, socle | C2×C32×C31 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
| maximal subgroup of | C32×C5×Dic31⋊C5, C32×ΓL(1,𝔽32)⋊Dic5, C32×ΓL(1,𝔽32)⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C32×C5×Dic31⋊C5 |
| maximal quotient of | C32×Dic31⋊C25, C32×C5×Dic31⋊C5, C32×ΓL(1,𝔽32)⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 61);